Full-rank representations of outer inverses based on the QR decomposition

An efficient algorithm for computing AT,S(2) inverses of a given constant matrix A, based on the QR decomposition of an appropriate matrix W  , is presented. Correlations between the derived representation of outer inverses and corresponding general representation based on arbitrary full-rank factorization are derived. In particular cases we derive representations of {2,4}{2,4} and {2,3}{2,3}-inverses. Numerical examples on different test matrices (dense or sparse) are presented as well as the comparison with several well-known methods for computing the Moore–Penrose inverse and the Drazin inverse.